论文标题
结节曲线和具有良好特性的极化
Nodal curves and polarizations with good properties
论文作者
论文摘要
在本文中，我们处理具有光滑组件的节点曲线$ c $上的极化。我们的目的是研究和描述一类极化，我们称之为“良好”，对于$ c $的深度，它反映了某些属性，这些属性适用于平滑曲线上的矢量束。我们将特别关注$ \ usevenline {w} $ - $ \ mathcal {o} _c $的稳定性与$ \ usewessline {w} $之间的关系。我们证明，这两个概念同意何时$ c $是紧凑的类型，并且我们猜想所有节点曲线都应相同。
In this paper we deal with polarizations on a nodal curve $C$ with smooth components. Our aim is to study and characterize a class of polarizations, which we call "good", for which depth one sheaves on $C$ reflect some properties that hold for vector bundles on smooth curves. We will concentrate, in particular, on the relation between the $\underline{w}$-stability of $\mathcal{O}_C$ and the goodness of $\underline{w}$. We prove that these two concepts agree when $C$ is of compact type and we conjecture that the same should hold for all nodal curves.
